The broad objectives of this research are the development of efficient methods of estimation in non- and semi parametric models for the analysis of censored survival data commonly present in biomedical studies. Although considerable progress has been made toward fitting such models to censored data, satisfactory solutions to important issues are still lacking. For example, a simple procedure is possible for estimating a survival function in the missing censoring indicator (MCI) model of random censorship, which has not been investigated and implemented so far. Furthermore some recently proposed semiparametric median and survival-rate regression models have not been explored for analyzing doubly censored data. In fact the utility of such regression models for the analysis of the relatively simpler right-censored data has been studied only for the special discrete covariate setting or for the special cases when the censoring or the observation error is independent of the covariate. The research objectives of this proposal are (A) Develop a new, simple-to-calculate, and asymptotically efficient nonparametric estimator of a survival function in the MCI model. (B) Initiate a methodology for fitting median regression models to analyze doubly censored data. (C) Develop for the case of continuous covariates the missing information principle (MIP) and the inverse censoring weighted (ICW) approaches of fitting right-censored (i) median regression models and (ii) survival-rate regression models. The research will focus on flexible and robust estimation methods, resulting in estimators that will be asymptotically efficient or will perform as well as or better than currently existing ones. Large sample properties of the estimators will be studied using nonparametric kernel estimation techniques, U-statistic theory, and other related large sample theory used in statistics and probability. Optimal bandwidths for computing the various estimators will be obtained by employing smoothed and other bootstrap ideas proposed in the literature. Preliminary theoretical and numerical studies justify the promise of the proposed approaches to have definite efficiency and robustness advantages over competing estimators. More extensive simulation studies will be carried out to study the operating characteristics of the proposed estimators. The project will illustrate the practical usefulness of the procedures by analyzing publicly available real data sets obtained from cancer and other health studies. The proposed research will extend significantly the current state of knowledge in the fitting of non- and semiparametric models to censored data. The software developed for the project will be made available for public use on a web site created specially for this purpose. [unreadable] [unreadable]